A number, n, is prime if n has no integer divisors other than 1 and itself.
- The first five prime numbers are: {2, 3, 5, 7, 11}.
A number, n, is composite if n has integer divisors other than 1 and itself.
- The first five composite numbers are: {4, 6, 8, 9, 10}.
These categories are clearly mutually exclusive, and one can be defined by the other.
A sieve is an algorithm or program that computes primes, typically in a range given as input.
Rhind Papyrus image from Wikipedia expressin different forms of primes/composites.